Question

I f k^1/2 = integer and k^1/4 = integer, which is a possible value for k?

Answer 1

Option D: 81 is the correct answer

Step-by-step explanation:

We have to find a number from the given options whose exponent 1/2 and 1/4 are integers.

First of all we have to exclude first two options with negative numbers as the exponents applied to these numbers will also give a negative number. So option A and option B are excluded

Now

for option C:

32 cannot be written as a square of any number so it is also excluded

We have to check the last option D: 81

Verification:

$(81) ^{\frac{1}{2}} = ?\\=(9^2)^{\frac{1}{2}}\\= 9^{(2*\frac{1}{2})}\\= 9$

$(81) ^{\frac{1}{4}} = ?\\=(3^4)^{\frac{1}{4}}\\= 3^{(4*\frac{1}{4})}\\= 3$

We can see that in cases of both exponents the number is an integer so

Option D: 81 is the correct answer

Keywords: Exponents, integers

Learn more about exponents at:

• brainly.com/question/10666510
• brainly.com/question/10699220

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